In vivo kinetics of SARS-CoV-2 infection and its relationship with a person's infectiousness

Modeling the transmission mitigation impact of testing for infectious diseases

A fundamental question of any program focused on the testing and timely diagnosis of a communicable disease is its effectiveness in reducing transmission. Here, we introduce testing effectiveness (TE)-the fraction by which testing and post-diagnosis isolation reduce transmission at the population scale-and a model that incorporates test specifications and usage, within-host pathogen dynamics, and human behaviors to estimate TE. Using TE to guide recommendations, we show that today's rapid diagnostics should be used immediately upon symptom onset to control influenza A and respiratory syncytial virus but delayed by up to two days to control omicron-era severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Furthermore, while rapid tests are superior to reverse transcription quantitative polymerase chain reaction (RT-qPCR) to control founder-strain SARS-CoV-2, omicron-era changes in viral kinetics and rapid test sensitivity cause a reversal, with higher TE for RT-qPCR despite longer turnaround times. Last, we illustrate the model's flexibility by quantifying trade-offs in the use of post-diagnosis testing to shorten isolation times.

Identifiability investigation of within-host models of acute virus infection

Uncertainty in parameter estimates from fitting within-host models to empirical data limits the model's ability to uncover mechanisms of infection, disease progression, and to guide pharmaceutical interventions. Understanding the effect of model structure and data availability on model predictions is important for informing model development and experimental design. To address sources of uncertainty in parameter estimation, we use four mathematical models of influenza A infection with increased degrees of biological realism. We test the ability of each model to reveal its parameters in the presence of unlimited data by performing structural identifiability analyses. We then refine the results by predicting practical identifiability of parameters under daily influenza A virus titers alone or together with daily adaptive immune cell data. Using these approaches, we present insight into the sources of uncertainty in parameter estimation and provide guidelines for the types of model assumptions, optimal experimental design, and biological information needed for improved predictions.

Incorporating Intracellular Processes in Virus Dynamics Models

In-host models have been essential for understanding the dynamics of virus infection inside an infected individual. When used together with biological data, they provide insight into viral life cycle, intracellular and cellular virus-host interactions, and the role, efficacy, and mode of action of therapeutics. In this review, we present the standard model of virus dynamics and highlight situations where added model complexity accounting for intracellular processes is needed. We present several examples from acute and chronic viral infections where such inclusion in explicit and implicit manner has led to improvement in parameter estimates, unification of conclusions, guidance for targeted therapeutics, and crossover among model systems. We also discuss trade-offs between model realism and predictive power and highlight the need of increased data collection at finer scale of resolution to better validate complex models.

Viral Kinetics Model of SARS-CoV-2 Infection Informs Drug Discovery, Clinical Dose, and Regimen Selection

Quantitative systems pharmacology (QSP) has been an important tool to project safety and efficacy of novel or repurposed therapies for the SARS-CoV-2 virus. Here, we present a QSP modeling framework to predict response to antiviral therapeutics with three mechanisms of action (MoA): cell entry inhibitors, anti-replicatives, and neutralizing biologics. We parameterized three distinct model structures describing virus-host interaction by fitting to published viral kinetics data of untreated COVID-19 patients. The models were used to test theoretical behaviors and map therapeutic design criteria of the different MoAs, identifying the most rapid and robust antiviral activity from neutralizing biologic and anti-replicative MoAs. We found good agreement between model predictions and clinical viral load reduction observed with anti-replicative nirmatrelvir/ritonavir (Paxlovid®) and neutralizing biologics bamlanivimab and casirivimab/imdevimab (REGEN-COV®), building confidence in the modeling framework to inform a dose selection. Finally, the model was applied to predict antiviral response with ensovibep, a novel DARPin therapeutic designed as a neutralizing biologic. We developed a new in silico measure of antiviral activity, area under the curve (AUC) of free spike protein concentration, as a metric with larger dynamic range than viral load reduction. By benchmarking to bamlanivimab predictions, we justified dose levels of 75, 225, and 600 mg ensovibep to be administered intravenously in a Phase 2 clinical investigation. Upon trial completion, we found model predictions to be in good agreement with the observed patient data. These results demonstrate the utility of this modeling framework to guide the development of novel antiviral therapeutics.

A retrospective cohort study of Paxlovid efficacy depending on treatment time in hospitalized COVID-19 patients

Paxlovid, a SARS-CoV-2 antiviral, not only prevents severe illness but also curtails viral shedding, lowering transmission risks from treated patients. By fitting a mathematical model of within-host Omicron viral dynamics to electronic health records data from 208 hospitalized patients in Hong Kong, we estimate that Paxlovid can inhibit over 90% of viral replication. However, its effectiveness critically depends on the timing of treatment. If treatment is initiated three days after symptoms first appear, we estimate a 17% chance of a post-treatment viral rebound and a 12% (95% CI: 0-16%) reduction in overall infectiousness for non-rebound cases. Earlier treatment significantly elevates the risk of rebound without further reducing infectiousness, whereas starting beyond five days reduces its efficacy in curbing peak viral shedding. Among the 104 patients who received Paxlovid, 62% began treatment within an optimal three-to-five-day day window after symptoms appeared. Our findings indicate that broader global access to Paxlovid, coupled with appropriately timed treatment, can mitigate the severity and transmission of SARS-Cov-2.

A joint Bayesian hierarchical model for estimating SARS-CoV-2 genomic and subgenomic RNA viral dynamics and seroconversion

Understanding the viral dynamics of and natural immunity to the severe acute respiratory syndrome coronavirus 2 is crucial for devising better therapeutic and prevention strategies for coronavirus disease 2019 (COVID-19). Here, we present a Bayesian hierarchical model that jointly estimates the genomic RNA viral load, the subgenomic RNA (sgRNA) viral load (correlated to active viral replication), and the rate and timing of seroconversion (correlated to presence of antibodies). Our proposed method accounts for the dynamical relationship and correlation structure between the two types of viral load, allows for borrowing of information between viral load and antibody data, and identifies potential correlates of viral load characteristics and propensity for seroconversion. We demonstrate the features of the joint model through application to the COVID-19 post-exposure prophylaxis study and conduct a cross-validation exercise to illustrate the model's ability to impute the sgRNA viral trajectories for people who only had genomic RNA viral load data.

Heterogeneous SARS-CoV-2 kinetics due to variable timing and intensity of immune responses

The viral kinetics of documented SARS-CoV-2 infections exhibit a high degree of interindividual variability. We identified 6 distinct viral shedding patterns, which differed according to peak viral load, duration, expansion rate, and clearance rate, by clustering data from 768 infections in the National Basketball Association cohort. Omicron variant infections in previously vaccinated individuals generally led to lower cumulative shedding levels of SARS-CoV-2 than other scenarios. We then developed a mechanistic mathematical model that recapitulated 1,510 observed viral trajectories, including viral rebound and cases of reinfection. Lower peak viral loads were explained by a more rapid and sustained transition of susceptible cells to a refractory state during infection as well as by an earlier and more potent late, cytolytic immune response. Our results suggest that viral elimination occurs more rapidly during Omicron infection, following vaccination, and following reinfection due to enhanced innate and acquired immune responses. Because viral load has been linked with COVID-19 severity and transmission risk, our model provides a framework for understanding the wide range of observed SARS-CoV-2 infection outcomes.

Predicting the presence of infectious virus from PCR data: A meta-analysis of SARS-CoV-2 in non-human primates

Researchers and clinicians often rely on molecular assays like PCR to identify and monitor viral infections, instead of the resource-prohibitive gold standard of viral culture. However, it remains unclear when (if ever) PCR measurements of viral load are reliable indicators of replicating or infectious virus. The recent popularity of PCR protocols targeting subgenomic RNA for SARS-CoV-2 has caused further confusion, as the relationships between subgenomic RNA and standard total RNA assays are incompletely characterized and opinions differ on which RNA type better predicts culture outcomes. Here, we explore these issues by comparing total RNA, subgenomic RNA, and viral culture results from 24 studies of SARS-CoV-2 in non-human primates (including 2167 samples from 174 individuals) using custom-developed Bayesian statistical models. On out-of-sample data, our best models predict subgenomic RNA positivity from total RNA data with 91% accuracy, and they predict culture positivity with 85% accuracy. Further analyses of individual time series indicate that many apparent prediction errors may arise from issues with assay sensitivity or sample processing, suggesting true accuracy may be higher than these estimates. Total RNA and subgenomic RNA showed equivalent performance as predictors of culture positivity. Multiple cofactors (including exposure conditions, host traits, and assay protocols) influence culture predictions, yielding insights into biological and methodological sources of variation in assay outcomes-and indicating that no single threshold value applies across study designs. We also show that our model can accurately predict when an individual is no longer infectious, illustrating the potential for future models trained on human data to guide clinical decisions on case isolation. Our work shows that meta-analysis of in vivo data can overcome longstanding challenges arising from limited sample sizes and can yield robust insights beyond those attainable from individual studies. Our analytical pipeline offers a framework to develop similar predictive tools in other virus-host systems, including models trained on human data, which could support laboratory analyses, medical decisions, and public health guidelines.

Delay induced stability switch in a mathematical model of CD8 T-cell response to SARS-CoV-2 mediated by receptor ACE2

The pathogen SARS-CoV-2 binds to the receptor angiotensin-converting enzyme 2 (ACE2) of the target cells and then replicates itself through the host, eventually releasing free virus particles. After infection, the CD8 T-cell response is triggered and appears to play a critical role in the defense against virus infections. Infected cells and their activated CD8 T-cells can cause tissue damage. Here, we established a mathematical model of within-host SARS-CoV-2 infection that incorporates the receptor ACE2, the CD8 T-cell response, and the damaged tissues. According to this model, we can get the basic reproduction number R0 and the immune reproduction number R1. We provide the theoretical proof for the stability of the disease-free equilibrium, immune-inactivated equilibrium, and immune-activated equilibrium. Finally, our numerical simulations show that the time delay in CD8 T-cell production can induce complex dynamics such as stability switching. These results provide insights into the mechanisms of SARS-CoV-2 infection and may help in the development of effective drugs against COVID-19.

In silico identification of viral loads in cough-generated droplets - Seamless integrated analysis of CFPD-HCD-EWF

BACKGROUND AND OBJECTIVE

Respiratory diseases caused by respiratory viruses have significantly threatened public health worldwide. This study presents a comprehensive approach to predict viral dynamics and the generation of stripped droplets within the mucus layer of the respiratory tract during coughing using a larynx-trachea-bifurcation (LTB) model.

METHODS

This study integrates computational fluid-particle dynamics (CFPD), host-cell dynamics (HCD), and the Eulerian wall film (EWF) model to propose a potential means for seamless integrated analysis. The verified CFPD-HCD coupling model based on a 3D-shell model was used to characterize the severe acute respiratory syndrome, coronavirus 2 (SARS-CoV-2) dynamics in the LTB mucus layer, whereas the EWF model was employed to account for the interfacial fluid to explore the generation mechanism and trace the origin site of droplets exhaled during a coughing event of an infected host.

RESULTS

The results obtained using CFPD delineated the preferential deposition sites for droplets in the laryngeal and tracheal regions. Thus, the analysis of the HCD model showed that the viral load increased rapidly in the laryngeal region during the peak of infection, whereas there was a growth delay in the tracheal region (up to day 8 after infection). After two weeks of infection, the high viral load gradually migrated towards the glottic region. Interestingly, the EWF model demonstrated a high concentration of exhaled droplets originating from the larynx. The coupling technique indicated a concurrent high viral load in the mucus layer and site of origin of the exhaled droplets.

CONCLUSIONS

This interdisciplinary research underscores the seamless analysis from initial exposure to virus-laden droplets, the dynamics of viral infection in the LTB mucus layer, and the re-emission from the coughing activities of an infected host. Our efforts aimed to address the complex challenges at the intersection of viral dynamics and respiratory health, which can contribute to a more detailed understanding and targeted prevention of respiratory diseases.

Modeling the emergence of viral resistance for SARS-CoV-2 during treatment with an anti-spike monoclonal antibody

To mitigate the loss of lives during the COVID-19 pandemic, emergency use authorization was given to several anti-SARS-CoV-2 monoclonal antibody (mAb) therapies for the treatment of mild-to-moderate COVID-19 in patients with a high risk of progressing to severe disease. Monoclonal antibodies used to treat SARS-CoV-2 target the spike protein of the virus and block its ability to enter and infect target cells. Monoclonal antibody therapy can thus accelerate the decline in viral load and lower hospitalization rates among high-risk patients with variants susceptible to mAb therapy. However, viral resistance has been observed, in some cases leading to a transient viral rebound that can be as large as 3-4 orders of magnitude. As mAbs represent a proven treatment choice for SARS-CoV-2 and other viral infections, evaluation of treatment-emergent mAb resistance can help uncover underlying pathobiology of SARS-CoV-2 infection and may also help in the development of the next generation of mAb therapies. Although resistance can be expected, the large rebounds observed are much more difficult to explain. We hypothesize replenishment of target cells is necessary to generate the high transient viral rebound. Thus, we formulated two models with different mechanisms for target cell replenishment (homeostatic proliferation and return from an innate immune response antiviral state) and fit them to data from persons with SARS-CoV-2 treated with a mAb. We showed that both models can explain the emergence of resistant virus associated with high transient viral rebounds. We found that variations in the target cell supply rate and adaptive immunity parameters have a strong impact on the magnitude or observability of the viral rebound associated with the emergence of resistant virus. Both variations in target cell supply rate and adaptive immunity parameters may explain why only some individuals develop observable transient resistant viral rebound. Our study highlights the conditions that can lead to resistance and subsequent viral rebound in mAb treatments during acute infection.

A mathematical model for the within-host (re)infection dynamics of SARS-CoV-2

Interactions between SARS-CoV-2 and the immune system during infection are complex. However, understanding the within-host SARS-CoV-2 dynamics is of enormous importance for clinical and public health outcomes. Current mathematical models focus on describing the within-host SARS-CoV-2 dynamics during the acute infection phase. Thereby they ignore important long-term post-acute infection effects. We present a mathematical model, which not only describes the SARS-CoV-2 infection dynamics during the acute infection phase, but extends current approaches by also recapitulating clinically observed long-term post-acute infection effects, such as the recovery of the number of susceptible epithelial cells to an initial pre-infection homeostatic level, a permanent and full clearance of the infection within the individual, immune waning, and the formation of long-term immune capacity levels after infection. Finally, we used our model and its description of the long-term post-acute infection dynamics to explore reinfection scenarios differentiating between distinct variant-specific properties of the reinfecting virus. Together, the model's ability to describe not only the acute but also the long-term post-acute infection dynamics provides a more realistic description of key outcomes and allows for its application in clinical and public health scenarios.

Modeling the Transmission Mitigation Impact of Testing for Infectious Diseases

A fundamental question of any program focused on the testing and timely diagnosis of a communicable disease is its effectiveness in reducing transmission. Here, we introduce testing effectiveness (TE)-the fraction by which testing and post-diagnosis isolation reduce transmission at the population scale-and a model that incorporates test specifications and usage, within-host pathogen dynamics, and human behaviors to estimate TE. Using TE to guide recommendations, we show that today's rapid diagnostics should be used immediately upon symptom onset to control influenza A and respiratory syncytial virus (RSV), but delayed by up to 2d to control omicron-era SARS-CoV-2. Furthermore, while rapid tests are superior to RT-qPCR for control of founder-strain SARS-CoV-2, omicron-era changes in viral kinetics and rapid test sensitivity cause a reversal, with higher TE for RT-qPCR despite longer turnaround times. Finally, we illustrate the model's flexibility by quantifying tradeoffs in the use of post-diagnosis testing to shorten isolation times.

Detecting changes in generation and serial intervals under varying pathogen biology, contact patterns and outbreak response

The epidemiological characteristics of SARS-CoV-2 transmission have changed over the pandemic due to emergence of new variants. A decrease in the generation or serial intervals would imply a shortened transmission timescale and, hence, outbreak response measures would need to expand at a faster rate. However, there are challenges in measuring these intervals. Alongside epidemiological changes, factors like varying delays in outbreak response, social contact patterns, dependence on the growth phase of an outbreak, and effects of exposure to multiple infectors can also influence measured generation or serial intervals. To guide real-time interpretation of variant data, we simulated concurrent changes in the aforementioned factors and estimated the statistical power to detect a change in the generation and serial interval. We compared our findings to the reported decrease or lack thereof in the generation and serial intervals of different SARS-CoV-2 variants. Our study helps to clarify contradictory outbreak observations and informs the required sample sizes under certain outbreak conditions to ensure that future studies of generation and serial intervals are adequately powered.

Heterogeneous SARS-CoV-2 kinetics due to variable timing and intensity of immune responses

The viral kinetics of documented SARS-CoV-2 infections exhibit a high degree of inter-individual variability. We identified six distinct viral shedding patterns, which differed according to peak viral load, duration, expansion rate and clearance rate, by clustering data from 768 infections in the National Basketball Association cohort. Omicron variant infections in previously vaccinated individuals generally led to lower cumulative shedding levels of SARS-CoV-2 than other scenarios. We then developed a mechanistic mathematical model that recapitulated 1510 observed viral trajectories, including viral rebound and cases of reinfection. Lower peak viral loads were explained by a more rapid and sustained transition of susceptible cells to a refractory state during infection, as well as an earlier and more potent late, cytolytic immune response. Our results suggest that viral elimination occurs more rapidly during omicron infection, following vaccination, and following re-infection due to enhanced innate and acquired immune responses. Because viral load has been linked with COVID-19 severity and transmission risk, our model provides a framework for understanding the wide range of observed SARS-CoV-2 infection outcomes.

Quantifying the relationship between within-host dynamics and transmission for viral diseases of livestock

Understanding the population dynamics of an infectious disease requires linking within-host dynamics and between-host transmission in a quantitative manner, but this is seldom done in practice. Here a simple phenomenological model for viral dynamics within a host is linked to between-host transmission by assuming that the probability of transmission is related to log viral titre. Data from transmission experiments for two viral diseases of livestock, foot-and-mouth disease virus in cattle and swine influenza virus in pigs, are used to parametrize the model and, importantly, test the underlying assumptions. The model allows the relationship between within-host parameters and transmission to be determined explicitly through their influence on the reproduction number and generation time. Furthermore, these critical within-host parameters (time and level of peak titre, viral growth and clearance rates) can be computed from more complex within-host models, raising the possibility of assessing the impact of within-host processes on between-host transmission in a more detailed quantitative manner.

The effect of model structure and data availability on Usutu virus dynamics at three biological scales

Understanding the epidemiology of emerging pathogens, such as Usutu virus (USUV) infections, requires systems investigation at each scale involved in the host-virus transmission cycle, from individual bird infections, to bird-to-vector transmissions, and to USUV incidence in bird and vector populations. For new pathogens field data are sparse, and predictions can be aided by the use of laboratory-type inoculation and transmission experiments combined with dynamical mathematical modelling. In this study, we investigated the dynamics of two strains of USUV by constructing mathematical models for the within-host scale, bird-to-vector transmission scale and vector-borne epidemiological scale. We used individual within-host infectious virus data and per cent mosquito infection data to predict USUV incidence in birds and mosquitoes. We addressed the dependence of predictions on model structure, data uncertainty and experimental design. We found that uncertainty in predictions at one scale change predicted results at another scale. We proposed in silico experiments that showed that sampling every 12 hours ensures practical identifiability of the within-host scale model. At the same time, we showed that practical identifiability of the transmission scale functions can only be improved under unrealistically high sampling regimes. Instead, we proposed optimal experimental designs and suggested the types of experiments that can ensure identifiability at the transmission scale and, hence, induce robustness in predictions at the epidemiological scale.

Transmission Bottleneck Size Estimation from De Novo Viral Genetic Variation

Sequencing of viral infections has become increasingly common over the last decade. Deep sequencing data in particular have proven useful in characterizing the roles that genetic drift and natural selection play in shaping within-host viral populations. They have also been used to estimate transmission bottleneck sizes from identified donor-recipient pairs. These bottleneck sizes quantify the number of viral particles that establish genetic lineages in the recipient host and are important to estimate due to their impact on viral evolution. Current approaches for estimating bottleneck sizes exclusively consider the subset of viral sites that are observed as polymorphic in the donor individual. However, these approaches have the potential to substantially underestimate true transmission bottleneck sizes. Here, we present a new statistical approach for instead estimating bottleneck sizes using patterns of viral genetic variation that arise de novo within a recipient individual. Specifically, our approach makes use of the number of clonal viral variants observed in a transmission pair, defined as the number of viral sites that are monomorphic in both the donor and the recipient but carry different alleles. We first test our approach on a simulated dataset and then apply it to both influenza A virus sequence data and SARS-CoV-2 sequence data from identified transmission pairs. Our results confirm the existence of extremely tight transmission bottlenecks for these 2 respiratory viruses.

A simplicial epidemic model for COVID-19 spread analysis

Networks allow us to describe a wide range of interaction phenomena that occur in complex systems arising in such diverse fields of knowledge as neuroscience, engineering, ecology, finance, and social sciences. Until very recently, the primary focus of network models and tools has been on describing the pairwise relationships between system entities. However, increasingly more studies indicate that polyadic or higher-order group relationships among multiple network entities may be the key toward better understanding of the intrinsic mechanisms behind the functionality of complex systems. Such group interactions can be, in turn, described in a holistic manner by simplicial complexes of graphs. Inspired by these recently emerging results on the utility of the simplicial geometry of complex networks for contagion propagation and armed with a large-scale synthetic social contact network (also known as a digital twin) of the population in the U.S. state of Virginia, in this paper, we aim to glean insights into the role of higher-order social interactions and the associated varying social group determinants on COVID-19 propagation and mitigation measures.

The impact of trained immunity in respiratory viral infections

Epidemic peaks of respiratory viruses that co-circulate during the winter-spring seasons can be synchronous or asynchronous. The occurrence of temporal patterns in epidemics caused by some respiratory viruses suggests that they could negatively interact with each other. These negative interactions may result from a programme of innate immune memory, known as trained immunity, which may confer broad protective effects against respiratory viruses. It is suggested that stimulation of innate immune cells by a vaccine or a pathogen could induce their long-term functional reprogramming through an interplay between metabolic and epigenetic changes, which influence the transcriptional response to a secondary challenge. During the coronavirus disease 2019 pandemic, the circulation of most respiratory viruses was prevented by non-pharmacological interventions and then resumed at unusual periods once sanitary measures were lifted. With time, respiratory viruses should find again their own ecological niches. This transition period provides an opportunity to study the interactions between respiratory viruses at the population level.

Neutralizing Antibody Levels as a Correlate of Protection Against SARS-CoV-2 Infection: A Modeling Analysis

Although anti-severe acute respiratory syndrome-coronavirus 2 antibody kinetics have been described in large populations of vaccinated individuals, we still poorly understand how they evolve during a natural infection and how this impacts viral clearance. For that purpose, we analyzed the kinetics of both viral load and neutralizing antibody levels in a prospective cohort of individuals during acute infection with alpha variant. Using a mathematical model, we show that the progressive increase in neutralizing antibodies leads to a shortening of the half-life of both infected cells and infectious viral particles. We estimated that the neutralizing activity reached 90% of its maximal level within 11 days after symptom onset and could reduce the half-life of both infected cells and circulating virus by a 6-fold factor, thus playing a key role to achieve rapid viral clearance. Using this model, we conducted a simulation study to predict in a more general context the protection conferred by pre-existing neutralization titers, due to either vaccination or prior infection. We predicted that a neutralizing activity, as measured by 50% effective dose > 103 , could reduce by 46% the risk of having viral load detectable by standard polymerase chain reaction assays and by 98% the risk of having viral load above the threshold of infectiousness. Our model shows that neutralizing activity could be used to define correlates of protection against infection and transmission.

Computational Modeling Insights into Extreme Heterogeneity in COVID-19 Nasal Swab Data

Throughout the COVID-19 pandemic, an unprecedented level of clinical nasal swab data from around the globe has been collected and shared. Positive tests have consistently revealed viral titers spanning six orders of magnitude! An open question is whether such extreme population heterogeneity is unique to SARS-CoV-2 or possibly generic to viral respiratory infections. To probe this question, we turn to the computational modeling of nasal tract infections. Employing a physiologically faithful, spatially resolved, stochastic model of respiratory tract infection, we explore the statistical distribution of human nasal infections in the immediate 48 h of infection. The spread, or heterogeneity, of the distribution derives from variations in factors within the model that are unique to the infected host, infectious variant, and timing of the test. Hypothetical factors include: (1) reported physiological differences between infected individuals (nasal mucus thickness and clearance velocity); (2) differences in the kinetics of infection, replication, and shedding of viral RNA copies arising from the unique interactions between the host and viral variant; and (3) differences in the time between initial cell infection and the clinical test. Since positive clinical tests are often pre-symptomatic and independent of prior infection or vaccination status, in the model we assume immune evasion throughout the immediate 48 h of infection. Model simulations generate the mean statistical outcomes of total shed viral load and infected cells throughout 48 h for each "virtual individual", which we define as each fixed set of model parameters (1) and (2) above. The "virtual population" and the statistical distribution of outcomes over the population are defined by collecting clinically and experimentally guided ranges for the full set of model parameters (1) and (2). This establishes a model-generated "virtual population database" of nasal viral titers throughout the initial 48 h of infection of every individual, which we then compare with clinical swab test data. Support for model efficacy comes from the sampling of infection dynamics over the virtual population database, which reproduces the six-order-of-magnitude clinical population heterogeneity. However, the goal of this study is to answer a deeper biological and clinical question. What is the impact on the dynamics of early nasal infection due to each individual physiological feature or virus-cell kinetic mechanism? To answer this question, global data analysis methods are applied to the virtual population database that sample across the entire database and de-correlate (i.e., isolate) the dynamic infection outcome sensitivities of each model parameter. These methods predict the dominant, indeed exponential, driver of population heterogeneity in dynamic infection outcomes is the latency time of infected cells (from the moment of infection until onset of viral RNA shedding). The shedding rate of the viral RNA of infected cells in the shedding phase is a strong, but not exponential, driver of infection. Furthermore, the unknown timing of the nasal swab test relative to the onset of infection is an equally dominant contributor to extreme population heterogeneity in clinical test data since infectious viral loads grow from undetectable levels to more than six orders of magnitude within 48 h.

Mathematical methods for scaling from within-host to population-scale in infectious disease systems

Mathematical modellers model infectious disease dynamics at different scales. Within-host models represent the spread of pathogens inside an individual, whilst between-host models track transmission between individuals. However, pathogen dynamics at one scale affect those at another. This has led to the development of multiscale models that connect within-host and between-host dynamics. In this article, we systematically review the literature on multiscale infectious disease modelling according to PRISMA guidelines, dividing previously published models into five categories governing their methodological approaches (Garira (2017)), explaining their benefits and limitations. We provide a primer on developing multiscale models of infectious diseases.

Association between SARS-CoV-2 viral kinetics and clinical score evolution in hospitalized patients

The role of antiviral treatment in coronavirus disease 2019 hospitalized patients is controversial. To address this question, we analyzed simultaneously nasopharyngeal viral load and the National Early Warning Score 2 (NEWS-2) using an effect compartment model to relate viral dynamics and the evolution of clinical severity. The model is applied to 664 hospitalized patients included in the DisCoVeRy trial (NCT04315948; EudraCT 2020-000936-23) randomly assigned to either standard of care (SoC) or SoC + remdesivir. Then we use the model to simulate the impact of antiviral treatments on the time to clinical improvement, defined by a NEWS-2 score lower than 3 (in patients with NEWS-2 <7 at hospitalization) or 5 (in patients with NEWS-2 ≥7 at hospitalization), distinguishing between patients with low or high viral load at hospitalization. The model can fit well the different observed patients trajectories, showing that clinical evolution is associated with viral dynamics, albeit with large interindividual variability. Remdesivir antiviral activity was 22% and 78% in patients with low or high viral loads, respectively, which is not sufficient to generate a meaningful effect on NEWS-2. However, simulations predicted that antiviral activity greater than 99% could reduce by 2 days the time to clinical improvement in patients with high viral load, irrespective of the NEWS-2 score at hospitalization, whereas no meaningful effect was predicted in patients with low viral loads. Our results demonstrate that time to clinical improvement is associated with time to viral clearance and that highly effective antiviral drugs could hasten clinical improvement in hospitalized patients with high viral loads.

Standardization and Comparison of Emergency Use Authorized COVID-19 Assays and Testing Laboratories

Motivation

The motivation for this work was the need to establish a predefined cutoff based on genome copies per ml (GE/ml) rather than Ct, which can vary depending on the laboratory and assay used. A GE/ml-based threshold was necessary to define what constituted 'low positives" for samples that were included in data sets submitted to the FDA for emergency use approval for SARS-CoV-2 antigen tests.

Summary

SARS-CoV-2, the causal agent of the global COVID-19 pandemic, made its appearance at the end of 2019 and is still circulating in the population. The pandemic led to an urgent need for fast, reliable, and widely available testing. After December 2020, the emergence of new variants of SARS-CoV-2 led to additional challenges since new and existing tests had to detect variants to the same extent as the original Wuhan strain. When an antigen-based test is submitted to the Food and Drug Administration (FDA) for Emergency Use Authorization (EUA) consideration it is benchmarked against PCR comparator assays, which yield cycle threshold (CT) data as an indirect indicator of viral load - the lower the CT, the higher the viral load of the sample and the higher the CT, the lower the viral load. The FDA mandates that 10-20% of clinical samples used to evaluate the antigen test have to be low positive. Low positive, as defined by the FDA, are clinical samples in which the CT of the SARS-CoV-2 target gene is within 3 CT of the mean CT value of the approved comparator test's Limit of Detection (LOD). While all comparator tests are PCR-based, the results from different PCR assays used are not uniform. Results vary depending on assay platform, target gene, LOD and laboratory methodology. The emergence and dominance of the Omicron variant further challenged this approach as the fraction of low positive clinical samples dramatically increased as compared to earlier SARS-CoV-2 variants. This led to 20-40% of clinical samples having high CT values and therefore assays vying for an EUA were failing to achieve the 80% Percent Positive Agreement (PPA) threshold required. Here we describe the methods and statistical analyses used to establish a predefined cutoff, based on genome copies per ml (GE/ml) to classify samples as low positive (less than the cutoff GE/ml) or high positive (greater than the cutoff GE/mL). CT 30 for the E gene target using Cobas® SARS-CoV-2-FluA/B platform performed at TriCore Reference Laboratories, and this low positive cutoff value was used for two EUA authorizations. Using droplet digital PCR and methods described here, a value 49,447.72 was determined as the GE/ml equivalent for the low positive cutoff. The CT cutoff corresponding to 49447.72 GE/ml was determined across other platforms and laboratories. The methodology and statistical analysis described here can now be used for standardization of all comparators used for FDA submissions with a goal towards establishing uniform criteria for EUA authorization.

Analysis of the risk and pre-emptive control of viral outbreaks accounting for within-host dynamics: SARS-CoV-2 as a case study

In the era of living with COVID-19, the risk of localised SARS-CoV-2 outbreaks remains. Here, we develop a multiscale modelling framework for estimating the local outbreak risk for a viral disease (the probability that a major outbreak results from a single case introduced into the population), accounting for within-host viral dynamics. Compared to population-level models previously used to estimate outbreak risks, our approach enables more detailed analysis of how the risk can be mitigated through pre-emptive interventions such as antigen testing. Considering SARS-CoV-2 as a case study, we quantify the within-host dynamics using data from individuals with omicron variant infections. We demonstrate that regular antigen testing reduces, but may not eliminate, the outbreak risk, depending on characteristics of local transmission. In our baseline analysis, daily antigen testing reduces the outbreak risk by 45% compared to a scenario without antigen testing. Additionally, we show that accounting for heterogeneity in within-host dynamics between individuals affects outbreak risk estimates and assessments of the impact of antigen testing. Our results therefore highlight important factors to consider when using multiscale models to design pre-emptive interventions against SARS-CoV-2 and other viruses.

Epidemic dynamics with time-varying transmission risk reveal the role of disease stage-dependent infectiousness

A key characteristic of acute communicable diseases is the infectiousness that varies over time as the infection dynamics evolve within a host, which influences the risk of transmission in different stages of the disease. Despite the evidence of time-varying transmission risk, most dynamic models of epidemics assume a constant transmission rate during the infectious period. Recent work has shown the difference in epidemic dynamics when this assumption is relaxed and different transmission rates are used by discretizing the infectious period into multiple sub-periods. Here, we develop an age-structured model to integrate a continuous time-varying transmission risk, based on an established correlation between the viral dynamics and infectiousness profile. Taking into account the natural history and parameter estimates of COVID-19 caused by the original strain of SARS-CoV-2, we demonstrate the difference in temporal epidemic dynamics when a continuous time-varying transmission probability is used as compared to multiple constant transmission probabilities. Our results show a significant difference between the incidence curves in terms of the magnitude and peak time, even when the reproduction number and total number of infections are the same for continuous and discrete transmission probabilities. Finally, we demonstrate the spurious outcome of preventing an epidemic through the isolation of infectious individuals when constant transmission probabilities are used, highlighting the importance of integrating a continuous time-dependent transmission parameter in dynamic models. These findings suggest a more cautious interpretation of model outcomes, especially those that are intended to evaluate the effectiveness of interventions and inform policy decisions for disease mitigation strategies.

Modeling the emergence of viral resistance for SARS-CoV-2 during treatment with an anti-spike monoclonal antibody

The COVID-19 pandemic has led to over 760 million cases and 6.9 million deaths worldwide. To mitigate the loss of lives, emergency use authorization was given to several anti-SARS-CoV-2 monoclonal antibody (mAb) therapies for the treatment of mild-to-moderate COVID-19 in patients with a high risk of progressing to severe disease. Monoclonal antibodies used to treat SARS-CoV-2 target the spike protein of the virus and block its ability to enter and infect target cells. Monoclonal antibody therapy can thus accelerate the decline in viral load and lower hospitalization rates among high-risk patients with susceptible variants. However, viral resistance has been observed, in some cases leading to a transient viral rebound that can be as large as 3-4 orders of magnitude. As mAbs represent a proven treatment choice for SARS-CoV-2 and other viral infections, evaluation of treatment-emergent mAb resistance can help uncover underlying pathobiology of SARS-CoV-2 infection and may also help in the development of the next generation of mAb therapies. Although resistance can be expected, the large rebounds observed are much more difficult to explain. We hypothesize replenishment of target cells is necessary to generate the high transient viral rebound. Thus, we formulated two models with different mechanisms for target cell replenishment (homeostatic proliferation and return from an innate immune response anti-viral state) and fit them to data from persons with SARS-CoV-2 treated with a mAb. We showed that both models can explain the emergence of resistant virus associated with high transient viral rebounds. We found that variations in the target cell supply rate and adaptive immunity parameters have a strong impact on the magnitude or observability of the viral rebound associated with the emergence of resistant virus. Both variations in target cell supply rate and adaptive immunity parameters may explain why only some individuals develop observable transient resistant viral rebound. Our study highlights the conditions that can lead to resistance and subsequent viral rebound in mAb treatments during acute infection.

Modelling how increased Cathepsin B/L and decreased TMPRSS2 usage for cell entry by the SARS-CoV-2 Omicron variant may affect the efficacy and synergy of TMPRSS2 and Cathepsin B/L inhibitors

The SARS-CoV-2 Omicron variant harbours many mutations in its spike protein compared to the original SARS-CoV-2 strain, which may alter its ability to enter cells, cell tropism, and response to interventions blocking virus entry. To elucidate these effects, we developed a mathematical model of SARS-CoV-2 entry into target cells and applied it to analyse recent in vitro data. SARS-CoV-2 can enter cells via two pathways, one using the host proteases Cathepsin B/L and the other using the host protease TMPRSS2. We found enhanced entry efficiency of the Omicron variant in cells where the original strain preferentially used Cathepsin B/L and reduced efficiency where it used TMPRSS2. The Omicron variant thus appears to have evolved to use the Cathepsin B/L pathway better but at the expense of its ability to use the TMPRSS2 pathway compared to the original strain. We estimated >4-fold enhanced efficiency of the Omicron variant in entry via the Cathepsin B/L pathway and >3-fold reduced efficiency via the TMPRSS2 pathway compared to the original or other strains in a cell type-dependent manner. Our model predicted that Cathepsin B/L inhibitors would be more efficacious and TMPRSS2 inhibitors less efficacious in blocking Omicron variant entry into cells than the original strain. Furthermore, model predictions suggested that drugs simultaneously targeting the two pathways would exhibit synergy. The maximum synergy and drug concentrations yielding it would differ for the Omicron variant compared to the original strain. Our findings provide insights into the cell entry mechanisms of the Omicron variant and have implications for intervention targeting these mechanisms.

Dynamical modelling of viral infection and cooperative immune protection in COVID-19 patients

Once challenged by the SARS-CoV-2 virus, the human host immune system triggers a dynamic process against infection. We constructed a mathematical model to describe host innate and adaptive immune response to viral challenge. Based on the dynamic properties of viral load and immune response, we classified the resulting dynamics into four modes, reflecting increasing severity of COVID-19 disease. We found the numerical product of immune system's ability to clear the virus and to kill the infected cells, namely immune efficacy, to be predictive of disease severity. We also investigated vaccine-induced protection against SARS-CoV-2 infection. Results suggested that immune efficacy based on memory T cells and neutralizing antibody titers could be used to predict population vaccine protection rates. Finally, we analyzed infection dynamics of SARS-CoV-2 variants within the construct of our mathematical model. Overall, our results provide a systematic framework for understanding the dynamics of host response upon challenge by SARS-CoV-2 infection, and this framework can be used to predict vaccine protection and perform clinical diagnosis.

Making waves: Integrating wastewater surveillance with dynamic modeling to track and predict viral outbreaks

Wastewater surveillance has proved to be a valuable tool to track the COVID-19 pandemic. However, most studies using wastewater surveillance data revolve around establishing correlations and lead time relative to reported case data. In this perspective, we advocate for the integration of wastewater surveillance data with dynamic within-host and between-host models to better understand, monitor, and predict viral disease outbreaks. Dynamic models overcome emblematic difficulties of using wastewater surveillance data such as establishing the temporal viral shedding profile. Complementarily, wastewater surveillance data bypasses the issues of time lag and underreporting in clinical case report data, thus enhancing the utility and applicability of dynamic models. The integration of wastewater surveillance data with dynamic models can enhance real-time tracking and prevalence estimation, forecast viral transmission and intervention effectiveness, and most importantly, provide a mechanistic understanding of infectious disease dynamics and the driving factors. Dynamic modeling of wastewater surveillance data will advance the development of a predictive and responsive monitoring system to improve pandemic preparedness and population health.

Statistical Challenges When Analyzing SARS-CoV-2 RNA Measurements Below the Assay Limit of Quantification in COVID-19 Clinical Trials

Most clinical trials evaluating coronavirus disease 2019 (COVID-19) therapeutics include assessments of antiviral activity. In recently completed outpatient trials, changes in nasal severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) RNA levels from baseline were commonly assessed using analysis of covariance (ANCOVA) or mixed models for repeated measures (MMRM) with single imputation for results below assay lower limits of quantification (LLoQ). Analyzing changes in viral RNA levels with singly imputed values can lead to biased estimates of treatment effects. In this article, using an illustrative example from the ACTIV-2 trial, we highlight potential pitfalls of imputation when using ANCOVA or MMRM methods, and illustrate how these methods can be used when considering values Collapse

Key Words

• COVID-19
• SARS-CoV-2 RNA
• linear regression for censored data
• randomized trial

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MESH Headings

• Humans
• Antiviral Agents
• Biological Assay
• COVID-19
• RNA, Viral
• SARS-CoV-2/genetics

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Grants

• UM1 AI069424 NIAID NIH HHS
• UM1 AI068634 NIH HHS
• UM1 AI069481 NIAID NIH HHS
• UM1 AI106701 NIAID NIH HHS
• U01 AI069424 NIAID NIH HHS
• UM1 AI069412 NIAID NIH HHS
• UM1 AI068634 NIAID NIH HHS
• UM1 AI068636 NIAID NIH HHS
• National Institute of Allergy and Infectious Diseases
• National Institutes of Health

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Affiliation(s)

Carlee B Moser Center for Biostatistics in AIDS Research, Harvard T. H. Chan School of Public Health, Boston, Massachusetts, USA
Kara W Chew Department of Medicine, David Geffen School of Medicine, University of California, Los Angeles, Los Angeles, California, USA
Mark J Giganti Center for Biostatistics in AIDS Research, Harvard T. H. Chan School of Public Health, Boston, Massachusetts, USA
Jonathan Z Li Department of Medicine, Brigham and Women's Hospital, Harvard Medical School, Cambridge, Massachusetts, USA
Evgenia Aga Center for Biostatistics in AIDS Research, Harvard T. H. Chan School of Public Health, Boston, Massachusetts, USA
Justin Ritz Center for Biostatistics in AIDS Research, Harvard T. H. Chan School of Public Health, Boston, Massachusetts, USA
Alexander L Greninger Department of Laboratory Medicine and Pathology, University of Washington, Seattle, Washington, USA
Arzhang Cyrus Javan National Institutes of Health, Rockville, Maryland, USA
Rachel Bender Ignacio Department of Medicine, University of Washington, Seattle, Washington, USA
Eric S Daar Lundquist Institute at Harbor-University of California, Los Angeles Medical Center, Torrance, California, USA
David A Wohl Department of Medicine, Chapel Hill School of Medicine, University of North Carolina, Chapel Hill, North Carolina, USA
Judith S Currier Department of Medicine, David Geffen School of Medicine, University of California, Los Angeles, Los Angeles, California, USA
Joseph J Eron Department of Medicine, Chapel Hill School of Medicine, University of North Carolina, Chapel Hill, North Carolina, USA
Davey M Smith Department of Medicine, University of California, San Diego, La Jolla, California, USA
Michael D Hughes Center for Biostatistics in AIDS Research, Harvard T. H. Chan School of Public Health, Boston, Massachusetts, USA Department of Biostatistics, Harvard T. H. Chan School of Public Health, Boston, Massachusetts, USA

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Variant-Specific Viral Kinetics in Acute COVID-19

Understanding variant-specific differences in severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) viral kinetics may explain differences in transmission efficiency and provide insights on pathogenesis and prevention. We evaluated SARS-CoV-2 kinetics from nasal swabs across multiple variants (Alpha, Delta, Epsilon, Gamma) in placebo recipients of the ACTIV-2/A5401 trial. Delta variant infection led to the highest maximum viral load and shortest time from symptom onset to viral load peak. There were no significant differences in time to viral clearance across the variants. Viral decline was biphasic with first- and second-phase decays having half-lives of 11 hours and 2.5 days, respectively, with differences among variants, especially in the second phase. These results suggest that while variant-specific differences in viral kinetics exist, post-peak viral load all variants appeared to be efficiently cleared by the host. Clinical Trials Registration. NCT04518410.

Transmission bottleneck size estimation from de novo viral genetic variation

Sequencing of viral infections has become increasingly common over the last decade. Deep sequencing data in particular have proven useful in characterizing the roles that genetic drift and natural selection play in shaping within-host viral populations. They have also been used to estimate transmission bottleneck sizes from identified donor-recipient pairs. These bottleneck sizes quantify the number of viral particles that establish genetic lineages in the recipient host and are important to estimate due to their impact on viral evolution. Current approaches for estimating bottleneck sizes exclusively consider the subset of viral sites that are observed as polymorphic in the donor individual. However, allele frequencies can change dramatically over the course of an individual's infection, such that sites that are polymorphic in the donor at the time of transmission may not be polymorphic in the donor at the time of sampling and allele frequencies at donor-polymorphic sites may change dramatically over the course of a recipient's infection. Because of this, transmission bottleneck sizes estimated using allele frequencies observed at a donor's polymorphic sites may be considerable underestimates of true bottleneck sizes. Here, we present a new statistical approach for instead estimating bottleneck sizes using patterns of viral genetic variation that arose de novo within a recipient individual. Specifically, our approach makes use of the number of clonal viral variants observed in a transmission pair, defined as the number of viral sites that are monomorphic in both the donor and the recipient but carry different alleles. We first test our approach on a simulated dataset and then apply it to both influenza A virus sequence data and SARS-CoV-2 sequence data from identified transmission pairs. Our results confirm the existence of extremely tight transmission bottlenecks for these two respiratory viruses, using an approach that does not tend to underestimate transmission bottleneck sizes.

Impact of variants of concern on SARS-CoV-2 viral dynamics in non-human primates

The impact of variants of concern (VoC) on SARS-CoV-2 viral dynamics remains poorly understood and essentially relies on observational studies subject to various sorts of biases. In contrast, experimental models of infection constitute a powerful model to perform controlled comparisons of the viral dynamics observed with VoC and better quantify how VoC escape from the immune response. Here we used molecular and infectious viral load of 78 cynomolgus macaques to characterize in detail the effects of VoC on viral dynamics. We first developed a mathematical model that recapitulate the observed dynamics, and we found that the best model describing the data assumed a rapid antigen-dependent stimulation of the immune response leading to a rapid reduction of viral infectivity. When compared with the historical variant, all VoC except beta were associated with an escape from this immune response, and this effect was particularly sensitive for delta and omicron variant (p<10-6 for both). Interestingly, delta variant was associated with a 1.8-fold increased viral production rate (p = 0.046), while conversely omicron variant was associated with a 14-fold reduction in viral production rate (p<10-6). During a natural infection, our models predict that delta variant is associated with a higher peak viral RNA than omicron variant (7.6 log10 copies/mL 95% CI 6.8-8 for delta; 5.6 log10 copies/mL 95% CI 4.8-6.3 for omicron) while having similar peak infectious titers (3.7 log10 PFU/mL 95% CI 2.4-4.6 for delta; 2.8 log10 PFU/mL 95% CI 1.9-3.8 for omicron). These results provide a detailed picture of the effects of VoC on total and infectious viral load and may help understand some differences observed in the patterns of viral transmission of these viruses.

Evolutionary safety of lethal mutagenesis driven by antiviral treatment

Nucleoside analogs are a major class of antiviral drugs. Some act by increasing the viral mutation rate causing lethal mutagenesis of the virus. Their mutagenic capacity, however, may lead to an evolutionary safety concern. We define evolutionary safety as a probabilistic assurance that the treatment will not generate an increased number of mutants. We develop a mathematical framework to estimate the total mutant load produced with and without mutagenic treatment. We predict rates of appearance of such virus mutants as a function of the timing of treatment and the immune competence of patients, employing realistic assumptions about the vulnerability of the viral genome and its potential to generate viable mutants. We focus on the case study of Molnupiravir, which is an FDA-approved treatment against Coronavirus Disease-2019 (COVID-19). We estimate that Molnupiravir is narrowly evolutionarily safe, subject to the current estimate of parameters. Evolutionary safety can be improved by restricting treatment with this drug to individuals with a low immunological clearance rate and, in future, by designing treatments that lead to a greater increase in mutation rate. We report a simple mathematical rule to determine the fold increase in mutation rate required to obtain evolutionary safety that is also applicable to other pathogen-treatment combinations.

Modelling the viral dynamics of the SARS-CoV-2 Delta and Omicron variants in different cell types

We use viral kinetic models fitted to viral load data from in vitro studies to explain why the SARS-CoV-2 Omicron variant replicates faster than the Delta variant in nasal cells, but slower than Delta in lung cells, which could explain Omicron's higher transmission potential and lower severity. We find that in both nasal and lung cells, viral infectivity is higher for Omicron but the virus production rate is higher for Delta, with an estimated approximately 200-fold increase in infectivity and 100-fold decrease in virus production when comparing Omicron with Delta in nasal cells. However, the differences are unequal between cell types, and ultimately lead to the basic reproduction number and growth rate being higher for Omicron in nasal cells, and higher for Delta in lung cells. In nasal cells, Omicron alone can enter via a TMPRSS2-independent pathway, but it is primarily increased efficiency of TMPRSS2-dependent entry which accounts for Omicron's increased activity. This work paves the way for using within-host mathematical models to understand the transmission potential and severity of future variants.

Competing Heterogeneities in Vaccine Effectiveness Estimation

Understanding the waning of vaccine-induced protection is important for both immunology and public health. Population heterogeneities in underlying (pre-vaccination) susceptibility and vaccine response can cause measured vaccine effectiveness (mVE) to change over time, even in the absence of pathogen evolution and any actual waning of immune responses. We use multi-scale agent-based models parameterized using epidemiological and immunological data, to investigate the effect of these heterogeneities on mVE as measured by the hazard ratio. Based on our previous work, we consider the waning of antibodies according to a power law and link it to protection in two ways: (1) motivated by correlates of risk data and (2) using a within-host model of stochastic viral extinction. The effect of the heterogeneities is given by concise and understandable formulas, one of which is essentially a generalization of Fisher's fundamental theorem of natural selection to include higher derivatives. Heterogeneity in underlying susceptibility accelerates apparent waning, whereas heterogeneity in vaccine response slows down apparent waning. Our models suggest that heterogeneity in underlying susceptibility is likely to dominate. However, heterogeneity in vaccine response offsets <10% to >100% (median of 29%) of this effect in our simulations. Our study suggests heterogeneity is more likely to 'bias' mVE downwards towards the faster waning of immunity but a subtle bias in the opposite direction is also plausible.

Antibody Dynamics Simulation-A Mathematical Exploration of Clonal Deletion and Somatic Hypermutation

We have employed mathematical modeling techniques to construct a comprehensive framework for elucidating the intricate response mechanisms of the immune system, facilitating a deeper understanding of B-cell clonal deletion and somatic hypermutation. Our improved model introduces innovative mechanisms that shed light on positive and negative selection processes during T-cell and B-cell development. Notably, clonal deletion is attributed to the attenuated immune stimulation exerted by self-antigens with high binding affinities, rendering them less effective in eliciting subsequent B-cell maturation and differentiation. Secondly, our refined model places particular emphasis on the crucial role played by somatic hypermutation in modulating the immune system's functionality. Through extensive investigation, we have determined that somatic hypermutation not only expedites the production of highly specific antibodies pivotal in combating microbial infections but also serves as a regulatory mechanism to dampen autoimmunity and enhance self-tolerance within the organism. Lastly, our model advances the understanding of the implications of antibody in vivo evolution in the overall process of organismal aging. With the progression of time, the age-associated amplification of autoimmune activity becomes apparent. While somatic hypermutation effectively delays this process, mitigating the levels of autoimmune response, it falls short of reversing this trajectory entirely. In conclusion, our advanced mathematical model offers a comprehensive and scholarly approach to comprehend the intricacies of the immune system. By encompassing novel mechanisms for selection, emphasizing the functional role of somatic hypermutation, and illuminating the consequences of in vivo antibody evolution, our model expands the current understanding of immune responses and their implications in aging.

Prolonged viral shedding from noninfectious individuals confounds wastewater-based epidemiology

Wastewater surveillance has been widely used to track and estimate SARS-CoV-2 incidence. While both infectious and recovered individuals shed virus into wastewater, epidemiological inferences using wastewater often only consider the viral contribution from the former group. Yet, the persistent shedding in the latter group could confound wastewater-based epidemiological inference, especially during the late stage of an outbreak when the recovered population outnumbers the infectious population. To determine the impact of recovered individuals' viral shedding on the utility of wastewater surveillance, we develop a quantitative framework that incorporates population-level viral shedding dynamics, measured viral RNA in wastewater, and an epidemic dynamic model. We find that the viral shedding from the recovered population can become higher than the infectious population after the transmission peak, which leads to a decrease in the correlation between wastewater viral RNA and case report data. Furthermore, the inclusion of recovered individuals' viral shedding into the model predicts earlier transmission dynamics and slower decreasing trends in wastewater viral RNA. The prolonged viral shedding also induces a potential delay in the detection of new variants due to the time needed to generate enough new cases for a significant viral signal in an environment dominated by virus shed by the recovered population. This effect is most prominent toward the end of an outbreak and is greatly affected by both the recovered individuals' shedding rate and shedding duration. Our results suggest that the inclusion of viral shedding from non-infectious recovered individuals into wastewater surveillance research is important for precision epidemiology.

An explanation for SARS-CoV-2 rebound after Paxlovid treatment

In a fraction of SARS-CoV-2 infected individuals treated with the oral antiviral Paxlovid, the virus rebounds following treatment. The mechanism driving rebound is not understood. Here, we show that viral dynamic models based on the hypothesis that Paxlovid treatment near the time of symptom onset halts the depletion of target cells, but may not fully eliminate the virus, which can lead to viral rebound. We also show that the occurrence of viral rebound is sensitive to model parameters, and the time treatment is initiated, which may explain why only a fraction of individuals develop viral rebound. Finally, the models are used to test the therapeutic effects of two alternative treatment schemes. These findings also provide a possible explanation for rebounds following other antiviral treatments for SARS-CoV-2.

Visual prediction and parameter optimization of viral dynamics in the mucus milieu of the upper airway based on CFPD-HCD analysis

BACKGROUND AND OBJECTIVE

Respiratory diseases caused by viruses are a major human health problem. To better control the infection and understand the pathogenesis of these diseases, this paper studied SARS-CoV-2, a novel coronavirus outbreak, as an example.

METHODS

Based on coupled computational fluid and particle dynamics (CFPD) and host-cell dynamics (HCD) analyses, we studied the viral dynamics in the mucus layer of the human nasal cavity-nasopharynx. To reproduce the effect of mucociliary movement on the diffusive and convective transport of viruses in the mucus layer, a 3D-shell model was constructed using CT data of the upper respiratory tract (URT) of volunteers. Considering the mucus environment, the HCD model was established by coupling the target cell-limited model with the convection-diffusion term. Parameter optimization of the HCD model is the key problem in the simulation. Therefore, this study focused on the parameter optimization of the viral dynamics model, divided the geometric model into multiple compartments, and used Monolix to perform the nonlinear mixed effects (NLME) of pharmacometrics to discuss the influence of factors such as the number of mucus layers, number of compartments, diffusion rate, and mucus flow velocity on the prediction results.

RESULTS

The findings showed that sufficient experimental data can be used to estimate the corresponding parameters of the HCD model. The optimized convection-diffusion case with a two-layer multi-compartment low-velocity model could accurately predict the viral dynamics.

CONCLUSIONS

Its visualization process could explain the symptoms of the disease in the nose and contribute to the prevention and targeted treatment of respiratory diseases.

Modeling identifies variability in SARS-CoV-2 uptake and eclipse phase by infected cells as principal drivers of extreme variability in nasal viral load in the 48 h post infection

The SARS-CoV-2 coronavirus continues to evolve with scores of mutations of the spike, membrane, envelope, and nucleocapsid structural proteins that impact pathogenesis. Infection data from nasal swabs, nasal PCR assays, upper respiratory samples, ex vivo cell cultures and nasal epithelial organoids reveal extreme variabilities in SARS-CoV-2 RNA titers within and between the variants. Some variabilities are naturally prone to clinical testing protocols and experimental controls. Here we focus on nasal viral load sensitivity arising from the timing of sample collection relative to onset of infection and from heterogeneity in the kinetics of cellular infection, uptake, replication, and shedding of viral RNA copies. The sources of between-variant variability are likely due to SARS-CoV-2 structural protein mutations, whereas within-variant population variability is likely due to heterogeneity in cellular response to that particular variant. With the physiologically faithful, agent-based mechanistic model of inhaled exposure and infection from (Chen et al., 2022), we perform statistical sensitivity analyses of the progression of nasal viral titers in the first 0-48 h post infection, focusing on three kinetic mechanisms. Model simulations reveal shorter latency times of infected cells (including cellular uptake, viral RNA replication, until the onset of viral RNA shedding) exponentially accelerate nasal viral load. Further, the rate of infectious RNA copies shed per day has a proportional influence on nasal viral load. Finally, there is a very weak, negative correlation of viral load with the probability of infection per virus-cell encounter, the model proxy for spike-receptor binding affinity.

Competing Heterogeneities in Vaccine Effectiveness Estimation

Understanding waning of vaccine-induced protection is important for both immunology and public health. Population heterogeneities in underlying (pre-vaccination) susceptibility and vaccine response can cause measured vaccine effectiveness (mVE) to change over time even in the absence of pathogen evolution and any actual waning of immune responses. We use a multi-scale agent-based models parameterized using epidemiological and immunological data, to investigate the effect of these heterogeneities on mVE as measured by the hazard ratio. Based on our previous work, we consider waning of antibodies according to a power law and link it to protection in two ways: 1) motivated by correlates of risk data and 2) using a within-host model of stochastic viral extinction. The effect of the heterogeneities is given by concise and understandable formulas, one of which is essentially a generalization of Fisher's fundamental theorem of natural selection to include higher derivatives. Heterogeneity in underlying susceptibility accelerates apparent waning, whereas heterogeneity in vaccine response slows down apparent waning. Our models suggest that heterogeneity in underlying susceptibility is likely to dominate. However, heterogeneity in vaccine response offsets <10% to >100% (median of 29%) of this effect in our simulations. Our methodology and results may be helpful in understanding competing heterogeneities and waning of immunity and vaccine-induced protection. Our study suggests heterogeneity is more likely to 'bias' mVE downwards towards faster waning of immunity but a subtle bias in the opposite direction is also plausible.

Stability of a delayed SARS-CoV-2 reactivation model with logistic growth and adaptive immune response

This paper develops and analyzes a SARS-CoV-2 dynamics model with logistic growth of healthy epithelial cells, CTL immune and humoral (antibody) immune responses. The model is incorporated with four mixed (distributed/discrete) time delays, delay in the formation of latent infected epithelial cells, delay in the formation of active infected epithelial cells, delay in the activation of latent infected epithelial cells, and maturation delay of new SARS-CoV-2 particles. We establish that the model's solutions are non-negative and ultimately bounded. We deduce that the model has five steady states and their existence and stability are perfectly determined by four threshold parameters. We study the global stability of the model's steady states using Lyapunov method. The analytical results are enhanced by numerical simulations. The impact of intracellular time delays on the dynamical behavior of the SARS-CoV-2 is addressed. We noted that increasing the time delay period can suppress the viral replication and control the infection. This could be helpful to create new drugs that extend the delay time period.

Safe CO2 threshold limits for indoor long-range airborne transmission control of COVID-19

CO₂-based infection risk monitoring is highly recommended during the current COVID-19 pandemic. However, the CO₂ monitoring thresholds proposed in the literature are mainly for spaces with fixed occupants. Determining CO₂ threshold is challenging in spaces with changing occupancy due to the co-existence of quanta and CO₂ remaining from previous occupants. Here, we propose a new calculation framework for deriving safe excess CO₂ thresholds (above outdoor level), C _t, for various spaces with fixed/changing occupancy and analyze the uncertainty involved. We categorized common indoor spaces into three scenarios based on their occupancy conditions, e.g., fixed or varying infection ratios (infectors/occupants). We proved that the rebreathed fraction-based model can be applied directly for deriving C _t in the case of a fixed infection ratio (Scenario 1 and Scenario 2). In the case of varying infection ratios (Scenario 3), C _t derivation must follow the general calculation framework due to the existence of initial quanta/excess CO₂. Otherwise, C _t can be significantly biased (e.g., 260 ppm) when the infection ratio varies greatly. C _t can vary significantly based on specific space factors such as occupant number, physical activity, and community prevalence, e.g., 7 ppm for gym and 890 ppm for lecture hall, indicating C _t must be determined on a case-by-case basis. An uncertainty of up to 6 orders of magnitude for C _t was found for all cases due to uncertainty in emissions of quanta and CO₂, thus emphasizing the role of accurate emissions data in determining C _t.

A quantitative systems pharmacology model of the pathophysiology and treatment of COVID-19 predicts optimal timing of pharmacological interventions

A quantitative systems pharmacology (QSP) model of the pathogenesis and treatment of SARS-CoV-2 infection can streamline and accelerate the development of novel medicines to treat COVID-19. Simulation of clinical trials allows in silico exploration of the uncertainties of clinical trial design and can rapidly inform their protocols. We previously published a preliminary model of the immune response to SARS-CoV-2 infection. To further our understanding of COVID-19 and treatment, we significantly updated the model by matching a curated dataset spanning viral load and immune responses in plasma and lung. We identified a population of parameter sets to generate heterogeneity in pathophysiology and treatment and tested this model against published reports from interventional SARS-CoV-2 targeting mAb and antiviral trials. Upon generation and selection of a virtual population, we match both the placebo and treated responses in viral load in these trials. We extended the model to predict the rate of hospitalization or death within a population. Via comparison of the in silico predictions with clinical data, we hypothesize that the immune response to virus is log-linear over a wide range of viral load. To validate this approach, we show the model matches a published subgroup analysis, sorted by baseline viral load, of patients treated with neutralizing Abs. By simulating intervention at different time points post infection, the model predicts efficacy is not sensitive to interventions within five days of symptom onset, but efficacy is dramatically reduced if more than five days pass post symptom onset prior to treatment.

The emergence of a virus variant: dynamics of a competition model with cross-immunity time-delay validated by wastewater surveillance data for COVID-19

We consider the dynamics of a virus spreading through a population that produces a mutant strain with the ability to infect individuals that were infected with the established strain. Temporary cross-immunity is included using a time delay, but is found to be a harmless delay. We provide some sufficient conditions that guarantee local and global asymptotic stability of the disease-free equilibrium and the two boundary equilibria when the two strains outcompete one another. It is shown that, due to the immune evasion of the emerging strain, the reproduction number of the emerging strain must be significantly lower than that of the established strain for the local stability of the established-strain-only boundary equilibrium. To analyze the unique coexistence equilibrium we apply a quasi steady-state argument to reduce the full model to a two-dimensional one that exhibits a global asymptotically stable established-strain-only equilibrium or global asymptotically stable coexistence equilibrium. Our results indicate that the basic reproduction numbers of both strains govern the overall dynamics, but in nontrivial ways due to the inclusion of cross-immunity. The model is applied to study the emergence of the SARS-CoV-2 Delta variant in the presence of the Alpha variant using wastewater surveillance data from the Deer Island Treatment Plant in Massachusetts, USA.

Statistical Challenges when Analyzing SARS-CoV-2 RNA Measurements Below the Assay Limit of Quantification in COVID-19 Clinical Trials

Most clinical trials evaluating COVID-19 therapeutics include assessments of antiviral activity. In recently completed outpatient trials, changes in nasal SARS-CoV-2 RNA levels from baseline were commonly assessed using analysis of covariance (ANCOVA) or mixed models for repeated measures (MMRM) with single-imputation for results below assay lower limits of quantification (LLoQ). Analyzing changes in viral RNA levels with singly-imputed values can lead to biased estimates of treatment effects. In this paper, using an illustrative example from the ACTIV-2 trial, we highlight potential pitfalls of imputation when using ANCOVA or MMRM methods, and illustrate how these methods can be used when considering values Collapse

Key Words

• sars-cov-2 rna
• covid-19
• linear regression for censored data
• randomized trial

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MESH Headings Collapse

Grants

• UM1 AI068634 NIAID NIH HHS
• UM1 AI068636 NIAID NIH HHS
• UM1 AI106701 NIAID NIH HHS

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Affiliation(s)

Carlee B Moser Center for Biostatistics in AIDS Research, Harvard T.H. Chan School of Public Health, Boston, 02115, USA
Kara W Chew Department of Medicine, David Geffen School of Medicine at University of California, Los Angeles, Los Angeles, 90024, USA
Mark J Giganti Center for Biostatistics in AIDS Research, Harvard T.H. Chan School of Public Health, Boston, 02115, USA
Jonathan Z Li Department of Medicine, Brigham and Women's Hospital, Harvard Medical School, Cambridge, 02139, USA
Evgenia Aga Center for Biostatistics in AIDS Research, Harvard T.H. Chan School of Public Health, Boston, 02115, USA
Justin Ritz Center for Biostatistics in AIDS Research, Harvard T.H. Chan School of Public Health, Boston, 02115, USA
Alexander L Greninger Department of Laboratory Medicine & Pathology, University of Washington, Seattle, 98195, USA
Arzhang Cyrus Javan National Institutes of Health, Rockville, 20852, USA Rachel Bender Ignacio, MD, MPH, Department of Medicine, University of Washington, Seattle, 98195, USA
Eric S Daar Lundquist Institute at Harbor-UCLA Medical Center, Torrance, 90502, USA David A Wohl, MD, Department of Medicine, University of North Carolina at Chapel Hill School of Medicine, Chapel Hill, 27599, USA
Judith S Currier Department of Medicine, David Geffen School of Medicine at University of California, Los Angeles, Los Angeles, 90024, USA
Joseph J Eron Department of Medicine, University of North Carolina at Chapel Hill School of Medicine, Chapel Hill, 27599, USA
Davey M Smith Department of Medicine, University of California, San Diego, La Jolla, 92093, USA
Michael D Hughes Department of Biostatistics and Center for Biostatistics in AIDS Research, Harvard T.H. Chan School of Public Health, Boston, 02115, USA For the ACTIV-2/A5401 Study Team

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Simplified within-host and Dose-response Models of SARS-CoV-2

Understanding the mechanistic dynamics of transmission is key to designing more targeted and effective interventions to limit the spread of infectious diseases. A well-described within-host model allows explicit simulation of how infectiousness changes over time at an individual level. This can then be coupled with dose-response models to investigate the impact of timing on transmission. We collected and compared a range of within-host models used in previous studies and identified a minimally-complex model that provides suitable within-host dynamics while keeping a reduced number of parameters to allow inference and limit unidentifiability issues. Furthermore, non-dimensionalised models were developed to further overcome the uncertainty in estimates of the size of the susceptible cell population, a common problem in many of these approaches. We will discuss these models, and their fit to data from the human challenge study (see Killingley et al. (2022)) for SARS-CoV-2 and the model selection results, which has been performed using ABC-SMC. The parameter posteriors have then used to simulate viral-load based infectiousness profiles via a range of dose-response models, which illustrate the large variability of the periods of infection window observed for COVID-19.